Metamath Proof Explorer


Theorem xmulcl

Description: Closure of extended real multiplication. (Contributed by Mario Carneiro, 20-Aug-2015)

Ref Expression
Assertion xmulcl ( ( 𝐴 ∈ ℝ*𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* )

Proof

Step Hyp Ref Expression
1 xmulf ·e : ( ℝ* × ℝ* ) ⟶ ℝ*
2 1 fovcl ( ( 𝐴 ∈ ℝ*𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* )